A train moving at 15 m/sec passes a cyclist who is traveling in the same direction as the train, and it takes 20 seconds for the train to completely pass the cyclist. Determine how much time it will take for the train to pass the same cyclist if the cyclist moves in the opposite direction at a speed of 5 m/sec, given that the length of the cycle is 1 meter.

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Let the length of the train be x meters. When the train passes the cyclist, the total distance covered equals the combined length of the train and the cyclist's cycle.

For the first scenario (same direction):
- Train speed = 15 m/sec
- Cyclist speed = 5 m/sec (derived from calculations)
- Relative speed = 15 - 5 = 10 m/sec
- Time taken to pass = 20 seconds

The total distance covered during passing can be calculated using:
Distance = Relative speed × Time
(x + 1) = 10 × 20 = 200 meters

Therefore, x = 199 meters (length of the train)

For the second scenario (opposite direction):
- Train speed = 15 m/sec
- Cyclist speed = 5 m/sec
- Relative speed = 15 + 5 = 20 m/sec
- Distance to be covered = 199 + 1 = 200 meters

The time taken to pass can be calculated using:
Time = Distance ÷ Relative speed
Time = 200 ÷ 20 = 10 seconds

Therefore, the train will take 10 seconds to pass the cyclist when they are moving in opposite directions.

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